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%I #16 Aug 26 2019 11:20:47
%S 1,5,30,205,1476,11070,85410,672605,5380830,43584804,356602950,
%T 2941974270,24441017580,204257075490,1715759433624,14476720225405,
%U 122626336026960,1042323856225470,8887182353111790,75985409119105764,651303506735164140,5595289216952336550
%N Bisection of A136704.
%C A sequence in Table 1 of Hao (1991) appears to match this sequence, but there are not enough terms there to be certain. It is possible that Hao's 1989 book will clarify things, but I do not have access to it.
%D Hao, Bai Lin, Elementary symbolic dynamics and chaos in dissipative systems. World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. xvi+460 pp. ISBN: 9971-50-682-3; 9971-50-698-X
%H Andrew Howroyd, <a href="/A253076/b253076.txt">Table of n, a(n) for n = 1..200</a>
%H Bai-lin Hao, <a href="https://www.researchgate.net/publication/239059727_Symbolic_dynamics_and_characterization_of_complexity-Physica_D_51">Symbolic dynamics and characterization of complexity</a>, Physica, D51 (1991), 161-176.
%F a(n) = (1/8*n) * Sum_{d|n, d odd} mu(d)*(3^(2*n/d) - 1). - _Andrew Howroyd_, Nov 11 2018
%t a[n_] := Sum[Boole[OddQ[d]] MoebiusMu[d] (3^(2n/d)-1), {d, Divisors[n]}]/(8n);
%t Array[a, 22] (* _Jean-François Alcover_, Aug 26 2019 *)
%o (PARI) a(n) = sumdiv(n>>valuation(n,2), d, moebius(d)*(3^(2*n/d)-1))/(8*n); \\ _Andrew Howroyd_, Nov 11 2018
%Y Cf. A136704, A253077.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 01 2015
%E Offset corrected and terms a(14) and beyond from _Andrew Howroyd_, Nov 11 2018
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